A quasi-one-dimensional mathematical theory is developed for determining the effects of rotation on the fluid flow and heat transfer in a cooling channel within a rotating gas turbine blade. The three-dimensional intricacies in the solutions of the same problem are captured through accurate computational fluid dynamic simulations. The derived analytical closed-form solutions predict the amount by which the relative total temperature of the coolant changes as a result of rotation. It is shown that such changes due to rotation are significant proportion of the change of coolant temperature due to heat transfer. The computed spatial evolutions of the primary velocity field, secondary velocity field and the force fields are presented as the coolant progresses from the inlet to the outlet so that the complexities and subtleties are exposed to a high degree of visualizability. Detailed considerations to various components of the centrifugal, Coriolis and pressure forces are given. The flow field is shown to depend strongly on whether the coolant moves in the spanwise outward or inward direction. The three-dimensionality of the flow field is reflected in complex circumferential variations of the blade temperature and the internal heat transfer coefficient. When the effects of the x–component of the Coriolis force interacts non-linearly with the effects of the z–component of the centrifugal force and a drastic x-gradient in fluid density due to a thin thermal boundary layer, then the primary velocity profile may exhibit great complexity, including flow separation. The present paper thus captures the strong, non-linear, two-way coupling between the fluid dynamics and heat transfer in the internal convective cooling occurring in a channel within a rotating gas turbine blade. Based on about 100 three-dimensional computational fluid dynamics simulations, new heat transfer correlations are developed for average Nusselt number for a rotating channel that will be of practical use.
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